2000/08/24 by Shinya Watanabe, Vachtang Putkaradze, Watanabe, Shinya +3
Engineering · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Heat Transfer #Fluid Dynamics and Thin Films #Fluid Dynamics and Turbulent Flows #Pattern Formation and Solitons (nlin.PS) #nlin.PS #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.physics/0008219
46 pages, latex 2.09, 10 PS figures included with psfig
arxiv created 2000/08/24 · openalex publication_date 2000/08/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study laminar thin film flows with large distortions in the free surface using the method of averaging across the flow. Two concrete problems are studied: the circular hydraulic jump and the flow down an inclined plane. For the circular hydraulic jump our method is able to handle an internal eddy and separated flow. Assuming a variable radial velocity profile like in Karman-Pohlhausen's method, we obtain a system of two ordinary differential equations for stationary states that can smoothly go through the jump where previous studies encountered a singularity. Solutions of the system are in good agreement with experiments. For the flow down an inclined plane we take a similar approach and derive a simple model in which the velocity profile is not restricted to a parabolic or self-similar form. Two types of solutions with large surface distortions are found: solitary, kink-like propagating fronts, obtained when the flow rate is suddenly changed, and stationary jumps, obtained, e.g., behind a sluice gate. We then include time-dependence in the model to study stability of these waves. This allows us to distinguish between sub- and supercritical flows by calculating dispersion relations for wavelengths of the order of the width of the layer.